Question

An S&P 500 index linked CD matures in 3 years, with the face value the same as the current S&P 500 index price, $ 1350. Upon its maturity, the investor will be paid back the face value, plus 80% of the gain on the S&P 500 index. The S&P 500 continuous dividend yield is 1.5% and continuously compounded risk-free rate is 6%. The S&P 500 volatility is 25%. What is the Black-Scholes price of the embedded option in this CD?

Answer 1

Market-linked CDs is an interesting instrument providing equity-like returns on the money to the investors without the risk of losing their principal in case the markets go down. In this context, there is a call option embedded in these types of CDs.

Provided the face value K of CD is same as the current S&P 500 index price in this particular Q, and the payoff of this embedded option if V is the fair value of CD at the time of maturity can be written as: -

Using Black-scholes Formulae,

• the value of underlying asset S is S&P index price $1,350,
• the exercise price K is the face value $1,350,
• the life of the option T is the life of CD 3 years,
• standard deviation in the value of the underlying asset is 25%, and
• riskless rate r is continuously compounded risk-free interest 6%

Using the formulae,

Calculating,

Putting in the values,

On simpliyfing,

Given the payoff is 80% of a call payoff, value of the embedded option is 80% of $312.300 = $249.84